1. The problem is to divide the mixed number 9 1/2 by 4. 2. First, convert the mixed number 9 1/2 to an improper fraction. The formula for converting a mixed number $a \frac{b}{c}$ to an improper fraction is $$\frac{a \times c + b}{c}$$. 3. Applying this, $$9 \frac{1}{2} = \frac{9 \times 2 + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2}$$. 4. Now, divide $$\frac{19}{2}$$ by 4. Dividing by a number is the same as multiplying by its reciprocal. So, $$\frac{19}{2} \div 4 = \frac{19}{2} \times \frac{1}{4}$$. 5. Multiply the numerators and denominators: $$\frac{19 \times 1}{2 \times 4} = \frac{19}{8}$$. 6. The fraction $$\frac{19}{8}$$ can be converted back to a mixed number by dividing 19 by 8: 19 ÷ 8 = 2 remainder 3, so $$\frac{19}{8} = 2 \frac{3}{8}$$. 7. Therefore, the final answer is $$2 \frac{3}{8}$$.